Question

A food store makes a 6-lb mixture of walnuts, cashews, and dates. The cost of walnuts is $1.50 per pound, cashews cost $1.00 per pound, and dates cost $1.50 per pound. The mixture calls for twice as many walnuts as cashews. The total cost of the mixture is $8.50. How much of each ingredient did the store use?

Answer 1

Answer:
3y + x = 6
4y + 1.50x = 8.50
Explanation:
Cost of walnut = $1.50
Cost of cashew = $1.00
Cost of dates = $1.50
Let
Dates = x
Cashew = y
Walnuts = 2y
Pounds of total mixture = 6 lb
Total cost of the mixture = $8.50
First equation (from Quantity)
Walnuts + cashew + dates = Total mixture
2y + y + x = 6
3y + x = 6
Second equation (from price× Quantity)
2y(1.50) + y(1.00) + x(1.50) = 8.50
3y + y + 1.50x = 8.50
4y + 1.50x = 8.50
Therefore, the system of equation to solve the question is
3y + x = 6
4y + 1.50x = 8.50